Find the Laplace Transform of each of the following functions.
s i n ( 2 t ) u ( t − τ )
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Find the Laplace Transform of each of the following functions. s i n ( 2 t...
B. Find the Laplace transform of the following functions. 1. f(t) = {" where n is a positive integer, 2. f(t) = { • 10<t< 0 <t< 3. f(t) = { t 0<t<1 2-t i<t<2 0 2<t<
Find the inverse Laplace transform of each of the following functions. a. F(s) = 4652 + 4) f(t) = c++{F(s)}(€) = [" 58 b. G(s) = 7 (s – 5)2(52 +36) g(t) = £•*{F(0)}(€) = *
1) Laplace transforms/Transfer functions Use Laplace transform tables!!!! 1.1: Find the Laplace transform of f(t) = (cos(2t) + e-4t)-u(t) (simplify into one ratio)
Find the inverse Laplace transform of each of the following functions. a. F(s) = 5 $4(s2 + 4) t f(t) = 2*4{F($)}(6) = dw b. G(s) = 4s (s + 5)2( 32 +81) g(t) = •{F()}(t) = dw
1) Laplace transforms/Transfer functions Use Laplace transform tables!!!! 1.1: Find the Laplace transform of - 4t) f(t) = lc + e *).u(t) (simplify into one ratio) 1.2.. Find the poles and zeros of the following functions. Indicate any repearted poles and complex conjugate poles. Expand the transforms using partial fraction expansion. 20 1.2.1: F(s) = (s + 3).(52 + 8 + 25) 1.2.2: 252 + 18s + 12 F(s) =- 54 + 9.5? + 34.5² + 90-s + 100
2. (8 points) Find the Laplace transform of each of the following functions. 1. 2 (t) = + cos 3+ + 3e-24 2. 2 (t) = (1 - *) (Hint: expand...) 3. 2 (t) = tsin? t (Hint: use half angle formula first...) 4. 2 (t) = cos(36) - 1
Find the Laplace transform of each of the following functions. 1. $(t) = f*(4(t – 1)* sin(67) dt L{v(t)}(s) = b. g(t) = [ e 2-3(t-1) cos(71) dT L{$(t)}(s) = c. y(t) = e5(t-1) sin(97) cos(6(t – T)) dt L{s(t)}(s) =
Question (2): Laplace Transformsa) Find the Laplace Transform of the following using the Laplace Transform table provided in the back:$$ f(t)=\frac{1}{4}\left(3 e^{-2 t}-8 e^{-4 t}+9 e^{-6 t}\right) u(t) $$b) Find the inverse Laplace Transform \(F(s)\) of the following function \(f(t)\) using the table:$$ f(t)=\frac{12 s^{2}(s+1)}{\left(8 s^{2}+5 s+800\right)(s+5)^{2}(10 s+8)} $$
Find the inverse Laplace transform of each of the following functions. In several of these problems, it will be helpful to write the functions 2 (as b)(cs2+ds +e) in the simpler form As B as2 + bs + c ds2+ es + f Cs+ D CsD and p2(s) = as + b T cs2 + ds + e 2
2. (8 points) Find the Laplace transform of each of the following functions. 1. 2 f(t) = 14 + cos 3t + 3e-2t 2. 2 h(t) = (1 - 3t)? (Hint: expand...) 3. 2 g(t) = t sin’t (Hint: use half angle formula first...) 4. 2 h(t) = e-2 cos(v3t) - tet